Short Bio

Kuldeep Meel is an Assistant Professor in the Computer Science Department of School of Computing at
National University of Singapore, where he holds Sung Kah Kay Assistant Professorship. The broader goal of his research is to advance artificial intelligence techniques, which utilize ubiquity of data and formal methods, to
enable computing to deal with increasingly uncertain real-world environments.

Two post-doc positions available in the broad area of applying machine learning to SAT solvers, approximate counting techniques, and CP. The position is available for one year and can be renewed for another year based on performance. Read advertisement for more details.I am looking for highly motivated Ph.D. students, research assistants, and interns (with time commitment of at least 6 months) in our group.
Read this before sending me an email.

As engineered systems expand, become more interdependent, and operate in real-time, reliability assessment is indispensable to support investment and decision making. However, network reliability problems are known to be #P-complete, a computational complexity class largely believed to be intractable. The computational intractability of network reliability motivates our quest for reliable approximations. Based on their theoretical foundations, available methods can be grouped as follows: (i) exact or bounds, (ii) guarantee-less sampling, and (iii) probably approximately correct (PAC). Group (i) is well regarded due to its useful byproducts, but it does not scale in practice. Group (ii) scales well and verifies desirable properties, such as the bounded relative error, but it lacks error guarantees. Group (iii) is of great interest when precision and scalability are required, as it harbors computationally feasible approximation schemes with PAC-guarantees. We give a comprehensive review of classical methods before introducing modern techniques and our developments. We introduce K-RelNet, an extended counting-based estimation method that delivers PAC-guarantees for the K-terminal reliability problem. Then, we test methods' performance using various benchmark systems. We highlight the range of application of algorithms and provide the foundation for future resilience engineering as it increasingly necessitates methods for uncertainty quantification in complex systems.

Probabilistic inference via model counting has emerged as a scalable technique with strong formal guarantees, thanks to recent advances in hashing-based approximate counting. State-of-the-art hashing-based counting algorithms use an {\NP} oracle, such that the number of oracle invocations grows linearly in the number of variables n in the input constraint. We present a new approach to hashing-based approximate model counting in which the number of oracle invocations grows logarithmically in $n$, while still providing strong theoretical guarantees. Our experiments show that the new approach outperforms state-of-the-art techniques for approximate counting by 1-2 orders of magnitude in running time.

3

On Computing Minimal Independent Support and Its Applications to Sampling and Counting
Alexander Ivrii, Sharad Malik, Kuldeep S. Meel, and Moshe Y. Vardi
Proceedings of International Conference on Constraint Programming (CP),2015.
Best Student Paper Award

Constrained sampling and counting are two fundamental problems arising in domains ranging from artificial intelligence and security, to hardware and software testing. Recent approaches to approximate solutions for these problems rely on employing SAT solvers and universal hash functions that are typically encoded as XOR constraints of length n/2 for an input formula with n variables. As the runtime performance of SAT solvers heavily depends on the length of XOR constraints, recent research effort has been focused on reduction of length of XOR constraints. Consequently, a notion of Independent Support was proposed, and it was shown that constructing XORs over independent support (if known) can lead to a significant reduction in the length of XOR constraints without losing the theoretical guarantees of sampling and counting algorithms. In this paper, we present the first algorithmic procedure (and a corresponding tool, called MIS) to determine minimal independent support for a given CNF formula by employing a reduction to group minimal unsatisfiable subsets (GMUS). By utilizing minimal independent supports computed by MIS, we provide new tighter bounds on the length of XOR constraints for constrained counting and sampling. Furthermore, the universal hash functions constructed from independent supports computed by MIS provide two to three orders of magnitude performance improvement in state-of-the-art constrained sampling and counting tools, while still retaining theoretical guarantees.

Given a CNF formula and a weight for each assignment of values to variables, two natural problems are weighted model counting and distribution-aware sampling of satisfying assignments. Both problems have a wide variety of important applications. Due to the inherent complexity of the exact versions of the problems, interest has focused on solving them approximately. Prior work in this area scaled only to small problems in practice, or failed to provide strong theoretical guarantees, or employed a computationally-expensive maximum a posteriori probability (MAP) oracle that assumes prior knowledge of a factored representation of the weight distribution. We present a novel approach that works with a black-box oracle for weights of assignments and requires only an {\NP}-oracle (in practice, a SAT-solver) to solve both the counting and sampling problems. Our approach works under mild assumptions on the distribution of weights of satisfying assignments, provides strong theoretical guarantees, and scales to problems involving several thousand variables. We also show that the assumptions can be significantly relaxed while improving computational efficiency if a factored representation of the weights is known.

3 Papers accepted at AAAI-19. The first paper, with Mate Soos, describes a new architecture for CNF-XOR formulas, which has allowed us to have a new approximate counter that is at least 100 times faster than ApproxMC2 – credit to Mate Soos for his breakthrough engineering that enabled this project! The second paper, with Sourav Chakraborty, proposes the first algorithmic framework to test the distribution of a sampler. We show that several samplers output distributions far from what they claim!
The third paper, with Supratik Chakraborty and Moshe Vardi, shows that several relaxations of probabilsitic inference do not give any computational advantage, raising concerns about the motivations behind their usage.

24 October 2018

Supratik Chakraborty has been awarded the IITB research award to recognize sustained work on a particular theme of research: constrained counting and sampling. Congratulations!

Recruitment

I am looking for highly motivated Ph.D. students and interns (with time commitment of at least 6 months) in our group.

If you are a student at NUS, feel free to drop by
my office or schedule a meeting with me. (See my calendar).

Otherwise, please send me an email with your CV if you are interested. Make sure your subject contains the word "olleh" and you should include reviews of two of the papers published in the previous 3 years at AAAI/IJCAI/CP/SAT/CAV conferences. The reviews should be in the body of the email (and not as pdf). Furthermore, the body of your email should contain the phrase: "Here are two papers that I have reviewed". You should also provide reason for your choice of the papers. A strong background in statistics, algorithms/formal methods and prior experience in coding is crucial to make a significant contribution to our research.